On Classes of Functions for which No Free Lunch Results Hold

Details On Classes of Functions for which No Free Lunch Results Hold On Classes of Functions for which No Free Lunch Results Hold

2001-08-21

arxiv.org/abs/cs/0108011v1

Computer Science

Neural and Evolutionary Computing

8 pages, 1 figure, see http://www.neuroinformatik.ruhr-uni-bochum.de/

Scientific paper

In a recent paper it was shown that No Free Lunch results hold for any subset F of the set of all possible functions from a finite set X to a finite set Y iff F is closed under permutation of X. In this article, we prove that the number of those subsets can be neglected compared to the overall number of possible subsets. Further, we present some arguments why problem classes relevant in practice are not likely to be closed under permutation.

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